Dame Elisabeth Murdoch, who died aged 103, was one of Australia's greatest philanthropists and mother of media tycoon Rupert Murdoch.

They had an affectionate relationship, often speaking three times a week. But she could go for days without looking at a newspaper, and voiced doubts about his hard-nosed approach to business.

There were also financial strains. In 2007 the Australian tax authorities claimed that changes Rupert had made to a family trust meant that his mother owed them $85m, though a decision in their favour by the administrative appeals tribunal was later reversed by the federal court.

Dame Elisabeth believed materialism had become "quite a menace. I am always thinking how fortunate I am to have the opportunity [for philanthropy] because the joy of giving is so wonderful." Yet although compassionate, she was no soft touch.

She was "devastated" when it was announced that Rupert and his second wife, Anna, were divorcing after 31 years, warning: "Rupert, you're going to be very, very lonely, and the first desiring female that comes along will snap you up."

He replied: "Don't be ridiculous, mum, I'm far too old for that" – he then met, and shortly afterwards married, Wendi Deng, 37 years his junior. Also, his mother was upset when he became an American citizen to advance his interests in the US; she was mollified, however, by his assurance that he was not intending to sell his Australian holdings.

A small, comely woman, she had the energy to fight a state premier or a bushfire – both of which she did – and in her 80s would sleep only four hours a night before rising to swim at dawn.

Cecil King, the head of IPC, which owned the Daily Mirror in London, was one of many who described her as first-class. "Women don't come better than that," he said. "A woman of integrity."

Elisabeth Joy Greene was born in Melbourne on February 8, 1909, the third daughter of Rupert Greene, a hard-drinking wool valuer, and Marie de Lancey Forth, a descendant of Nathaniel Parker Forth, the diplomat who worked as a British spy during the French Revolution.

Elisabeth was an 18-year-old debutante when Keith Murdoch, editor of the Melbourne Herald, saw her pensive picture in one of his magazines. A 42-year-old bachelor, he arranged to meet her, and they married in 1928, going on to have three daughters, as well as Rupert.

Within a few years her husband had become Sir Keith, chairman and managing director, and she, aged 24, was Lady Murdoch (to close friends "Lady Liz"). She liked to tell the story of a dinner with Herald staff at which her husband, who was proud of his antiques, asked a young woman: "Do you like old things?" "Oh yes, Sir Keith," she said nervously. "I'm very fond of you."

Although Sir Keith was an archetypal Australian Victorian, it was his wife who was the disciplinarian in the family. All four children had to take piano lessons, and she made her son sleep in a hut without heat, electricity or water – no great imposition, considering the climate, Rupert later conceded.

When Keith Murdoch died in 1952, she launched herself into an independent life.

Rupert wanted to settle his father's estate in a way that gave him a newspaper base in Brisbane, but she preferred to see the debts cleared, leaving a small group of papers in Adelaide; it was a decision he thought wrong and about which she remained uncertain.

Her charm helped to persuade William Carr, chairman of the News of the World, to accept Rupert's offer to become a shareholder. But when Rupert told her that The Sunday Times planned to publish Hitler's newly discovered diaries, she told him: "Rupert, you've been sold a pup."

As president of the management committee of the Royal Children's Hospital, Melbourne, she brought to a triumphant conclusion the design and funding of new premises for 400 beds. But when Henry Bolte, the premier of Victoria, learned that she wanted a new location, he said: "Well, Lady Murdoch, there is a strong opinion that we should rebuild on your present site in Carlton.

"Well, then, Mr Premier," she replied, "you will have to ask someone else to do it." She won, and when it was opened by the queen she was appointed DBE.

On her 70th birthday she was observed up a ladder decorating a marquee, and on her 80th she received an electric golf buggy – she said it would be useful to take her older friends around. On her 100th birthday she was given a party attended by more than 70 descendants as well as by some 400 guests. No press were admitted.

Dame Elisabeth is survived by her son and two daughters; her eldest daughter died in 2004. On the eve of her century she was photographed sniffing a Dame Elisabeth Murdoch rose, named in her honour, which she said flowered for about six months: "As tough as old boots," she declared. "Wonderful!"